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The circumference of a semicircle of area 693 cm² is equal to the breadth of a rectangle. What is the length of the rectangle if the perimeter of the rectangle is 480 cm?
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Given, area of the semicircle, ½πr² = 693
=> r² = 693 * 2 * 7/22 = 441
=> r = 21 cm
∴ Circumference of semicircle = (πr + 2r) = 22/7 * 21 + 2 * 21 = 108 cm
∴ Breadth of the rectangle = 108 cm
Perimeter of rectangle, 2(l + b) = 480
=> 2(l + 108) = 480
=> 2l + 216 = 480
=> 2l = 264
=> l = 132 cm
A certain sum is invested at simple interest and at compound interest for 2 years and the ratio of the interests obtained on simple interest to that on compound interest is 10:11. Find the rate of interest.
Simple interest when Principal is P and rate is r% and time 2 years= 2Pr/100 ..(1)
And the C.I for this period = P (1+ r/100)2 - P = P(r/100)2 + 2Pr/100 = Pr/100 (r/100 + 2)..(2)
Ratio of SI and CI = equation (1)/equation (2) = 2/(2 + r/100)
According to question, 10/11 = 2/(2+r/100)
22 = 20 + r/10 => r/10 = 2 => r = 20%
In the following questions, two statements numbered I and II are given. On solving them, we get quantities I and II respectively. Solve for both the quantities and choose the correct option.
Quantity I: In a group, there are 17 men and 12 women. If the average income per day of the woman is Rs 135 and average income per day of the group is 145 then what is the average income per day of a man in Rs?
Quantity II: In a company ratio of Engineers and Managers is 11: 2. If 24 Engineers departed then this ratio became 9: 2. What is the total number of Engineers and Managers in the company?
Quantity - I
Total income of the group = 145 x 29 = 4205
Total income of all the women = 12 x 135 - 1620
Average income per day of a man = (4205 - 1620)/17
= 2585/17 = 152.06 Rs
Quantity - II
Let, there are 13n employees in the company.
According to the question; (11n-24)/2n = 9/2
=>11n - 24 = 9n
=>2n = 24
=>n = 12
Quantity I: Marks obtained by Vinod in four subjects are in the ratio of 5 : 3 : 4 : 6. If the highest marks scored by Vinod in one of four subjects is 72 and the maximum marks that one can get is 100 then what is the average marks scored by Vinod in all the four subjects?
Quantity II: Marks obtained by Arpita in four subjects are in the ratio of 9: 15: 12: 10. If the lowest marks scored by Arpita is 54 and the maximum marks available in a subject is 100 then what is the average marks scored by Arpita in a subject?
Let the marks obtained by Vinod are 5n, 3n, 4n and 6n respectively.
According to the question; 6n = 72
=> n = 12
Total marks scored in all the four subjects = 18n
Average marks scored in one subject = 4.5n = 54
Let the marks obtained by Arpita are 9n, 15n, 12n and 10n respectively.
According to the question; 9n = 54
=> n = 6
Total marks scored in all the four subjects = 46n
Average marks scored in four subjects = 46n/4 = 11.5n = 69
Ankur is 3 times as old as his younger brother. Ankur's Uncle is 3 times as old as Ankur. 3 years from now, Ankur's Uncle will be 5 times the age of his younger brother. What will the sum of the ages of Ankur, Ankur's younger brother and Ankur's Uncle 10 years from now?
Let the ages of Ankur, his brother, and Uncle be A,B,U.
A = 3B, U = 3A or U = 9B
3 years from now, U+3 = 5(B+3)
Or, 9B + 3 = 5B + 15
4B = 12 or B = 3
So current ages are: 3,9,27
Sum 10 years from now = (3 + 9 + 27) + 10x3 (As all 3 grow older by 10 years)
= 69
The average salary of all the employees of a company is Rs 25000. The average salary of 22 managers is Rs 45000 and for the rest of the employees it is Rs 20000. What is the total number of employees in the company?
Let the number of rest of the employees = N
Total salary of all the managers = Rs (22 X 45000)
= Rs 990000
Total salary of rest of the employees = Rs 20000N
According to the question; (990000+20000N)/(22+N)=25000
=> 990 + 20N = 25(22 + N)
=> 990 + 20N = 550 + 25N
=> 440 = 5N
=> N = 88
Hence total number of employees in the company = (88 + 22) = 110
Ajit, Anand and Ayush enter into a partnership investing their Money in the ratio 3:4:5. What is the ratio of their time period of investments if Ayush receives Rs 15,000 as share from a profit of Rs 51,000? Given that Ajit invested for twice the time Ayush invested.
Let the time period of their investments be 2x:y:x
Profit will be shared in the ratio 6x:4y:5x
Given, (5x/(11x + 4y))*51000 = 15000
=> 5x/(11x + 4y) = 5/17
=> 85x = 55x + 20y
=> 30x = 20y
=> 3x = 2y
Let x = 2k and y = 3k
∴ Required ratio = 2x:y:x = 4k:3k:2k = 4:3:2
Find the wrong term in the series given below.
103, 174, 259, 364, 487
The pattern is as follows:
102 + 3 = 103
132 + 3 = 172
162 + 3 = 259
192 + 3 = 364
222 + 3 = 487
When a bicycle retailer reduced its selling price by 50%, the number of bicycles sold increased by 600%. If originally the retailer was getting 140% profit, what is the percentage increase in his profit?
Let the selling price of a bicycle be 240 and the number of bicycles sold be N
Profit = 140
Cost price = 100
Total profit = 140N
After reducing the selling price, SP = 120
And the number of bicycles sold = 7N
Profit = ((120-100)/100) * 100 = 20
Total profit = 20 X 7N = 140N
Hence, the profit remains same or profit increase = 0%
9217, 2305, 579, 145, 37, 10
(9217 + 3) / 4 = 2305
(2305 + 3) / 4 = 577
(577 + 3) / 4 = 145
(145 + 3) / 4 = 37
(37 + 3) / 4 = 10
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